| searching for absolute rest -
02-06-2006, 02:02 PM
Simultaneity is a very complicated word in mathematics and physics. The reason is its intimate relation to an absolute frame of reference that is motionless. Searching for it became the lifetime endeavor of many people. Einstein tried but failed. Nevertheless, his conclusion from special theory of relativity is that simultaneity does not exist for all inertial frames moving uniformly relative to each other. But if two or more of these are moving along a straight line at constant speed then they are relatively at rest with each other. This describes perfectly the frames for all light waves and photons but not for mass particles. In order to postulate an absolute frame for mass particles, Einstein spent ten more years working out his general theory which was finally resolved by his Principle of General Covariance in 1915. What is general covariance? It is an alternate version of the Principle of Equivalence. At face value it has to do solely with the coordinate systems of transformations such that the form of the equations using them remains invariance. That is equations that are independent of any coordinate systems. Regardless of this assertion, the generalized coordinates were taken from absolute differential calculus of tensor analysis. Tensor analysis deals with infinitesimal changes but nonetheless it was used by Einstein to solve his global large scale theory of gravity. It must be noted that general relativity, in spite of its accurate predictions, never resolved the question implied by Mach’s principle. Mach’s principle is a non-mathematical principle that asserts the interaction between the small and the large which were separated by enormous distances. Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c² |